To write the equation of a line perpendicular to the given equation, we first need to determine its slope. After that, we will write a general equation and use the given point to determine the y-intercept.
Calculating the Slope of the Perpendicular Line
Two lines are perpendicular when their slopes are negative reciprocals. This means that the product of a given slope and the slope of a line perpendicular to it will be -1.
m_1* m_2=-1
For any equation written in slope-intercept form, y= mx+ b, we can identify its slope as the value of m.
Since the given equation is not written in slope-intercept form, we will have to rewrite it before identifying the slope.
Now we are able to identify the slope and the y-intercept.
y= -2x+ 6
We can see that the slope is -2. By substituting this value into our negative reciprocal equation for m_1, we can solve for the slope of the perpendicular line m_2.
With this, we can identify that any line perpendicular to the given equation will have a slope of 12.
Writing the Equation of the Perpendicular Line
With the slope m_2= 12, we can write a general equation in slope-intercept form for all lines perpendicular to the given equation.
y= 1/2x+ b
By substituting the given point ( 8, 1) into this equation for x and y, we can solve for the y-intercept b of the perpendicular line.
Now that we have the y-intercept, we can write the equation of the line that is both perpendicular to 2y+4x=12 and passes through the point (8,1).
y= 1/2x -3
